Author ORCID Identifier

http://orcid.org/0000-0001-6728-3250

Degree Year

2018

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Advisor(s)

Elizabeth L. Wilmer

Keywords

Spectral graph theory, Eigenvalues, Interlacing inequalities

Abstract

Motivated by an effort to simplify the Watts-Strogatz model for small-world networks, we generalize a theorem concerning interlacing inequalities for the eigenvalues of the normalized Laplacians of two graphs differing by a single edge. Our generalization allows weighted edges and certain instances of self loops. These inequalities were first proved by Chen et. al in [2] but our argument generalizes the simplified argument given by Li in [8].

Included in

Mathematics Commons

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